Choice of initial guess in iterative solution of series of systems arising in fluid flow simulations

Journal of Computational Physics

Volumn 219, Issue 1, 2006, Pages 210-227

  Tromeur Dervout, Damien ^a,b   Vassilevski, Yuri ^c  

^a Center for the Development of Scientific Parallel Computing   (France)

^b UNIVERSITÉ LYON 1   (France)

^c INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

Author keywords

Inexact Newton methods; Krylov subspace methods; Unsteady Navier Stokes equations

Indexed keywords

FLOW OF FLUIDS; LINEAR SYSTEMS; NEWTON-RAPHSON METHOD; NONLINEAR EQUATIONS; PROBLEM SOLVING;

EVOLUTION PROBLEM; FLUID FLOW SIMULATION; INEXACT NEWTON METHOD; INITIAL GUESS; ITERATIVE SOLUTIONS; KRYLOV-SUBSPACE METHODS; NAVIER-STOKES EQUATION; NONLINEAR FLUIDS; TIME-STEPPING SCHEMES; UNSTEADY NAVI-STOKE EQUATION;

NAVIER STOKES EQUATIONS;

EID: 33750374486     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.03.014     Document Type: Article

References (36)

1. Axelsson O. Iterative Solution Methods (1996), Cambridge University Press, New York
2. Barrett R., Berry M., Chan T., Demmel J., Donato J., Dongarra J., Eijkhout V., Pozo R., Romine C., and der Vorst H.V. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (1994), SIAM, Philadelphia, PA
3. Bjorstad P. Fast numerical solution of the biharmonic Dirichlet problem on rectangles. SIAM J. Numer. Anal. 20 (1983) 59-71
4. Brown P., and Saad Y. Hybrid Krylov methods for nonlinear systems of equations. SIAM J. Sci. Statist. Comput. 11 (1990) 450-481
5. Chan T.F., and Wan W.L. Analysis of projection methods for solving linear systems with multiple right-hand sides. SIAM J. Sci. Comput. 1 6 (1997) 1698-1721
6. Drikakis D., Iliev O.P., and Vassileva D.P. A nonlinear multigrid method for the three-dimensional incompressible Navier-Stokes equations. J. Comput. Phys. 146 (1998) 301-321
7. Erhel J., and Guyomarc'h F. An augmented conjugate gradient method for solving consecutive symmetric positive definite linear systems. SIAM J. Matrix Anal. Appl. 2 4 (2000) 1279-1299
8. Fischer P.F. Projection techniques for iterative solution of Ax = b with successive right-hand sides. Comput. Methods Appl. Mech. Eng. 16 1-4 (1998) 193-204
9. Eisenstat S., and Walker H. Globally convergent inexact Newton methods. SIAM J. Optim. 4 (1994) 393-422
10. Eisenstat S., and Walker H. Choosing the forcing terms in an inexact Newton method. SIAM J. Sci. Comput. 17 (1996) 16-32
11. Feistauer M. Mathematical Methods in Fluid Dynamics. Pitman Monographs and Surveys in Pure and Applied Mathematics Series 67 (1993), Longman Scientific & Technical, Harlow
12. Garbey M., and Vassilevski Y. A parallel solver for unsteady incompressible 3D Navier-Stokes equations. Parallel Computing 27 (2001) 363-389
13. Glowinski R., and Pironneau O. Numerical methods for the first biharmonic equation and for the two-dimensional Stokes problem. SIAM Rev. 21 (1979) 167-212
14. Gosselet P., and Rey Ch. On a selective reuse of Krylov subspaces in Newton-Krylov approaches for nonlinear elasticity. Domain Decomposition Methods in Science and Engineering (2003), Natl. Auton. Univ. Mex., Mexico pp. 419-426
15. W. Gropp, L. Curfman McInnes, B. Smith, Using the scalable nonlinear equations solvers package, Technical Report ANL/MCS-TM-193, Argonne National Laboratory, Argonne, IL, 1995.
16. Kelley C.T. Iterative methods for optimization. Frontiers in Applied Mathematics 18 (1999), SIAM, Philadelphia
17. I. Keshtiban, F. Belblidia, M. Webster, Compressible flow solvers for Low Mach number flows - a review, Technical Report CSR2, Institute of Non-Newtonian Fluid Mechanics, University of Wales, Swansea, UK, 2004.
18. Kim J., and Moin P. Application of a fractional step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59 (1985) 308-323
19. Knoll D.A., and Keyes D.E. Jacobian-free Newton-Krylov methods: a survey of approaches and applications. J. Comput. Phys. 193 (2004) 357-397
20. Knoll D.A., and McHugh P.R. An inexact newton algorithm for solving the Tokamak edge plasma fluid equations on a multiply-connected domain. J. Comput. Phys. 116 (1995) 281-291
21. Kuznetsov Y. Numerical methods in subspaces. Computational Processes and Systems (1985), Nauka, Moscow pp. 265-350 (in Russian)
22. Lehoucq R., Sorensen D., and Yang C. ARPACK users' guide: solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods. Software, Environments, and Tools vol. 6 (1998), SIAM
23. Marchuk G., Kuznetsov Y., and Matsokin A. Fictitious domain and domain decomposition methods. Sov. J. Numer. Anal. Math. Modelling 1 (1986) 3-35
24. Marion M., and Temam R. Navier-Stokes equations: theory and approximation. Handbook of Numerical Analysis vol. VI (1998), Elsevier, Amsterdam pp. 503-689
25. Meurant G. Computer Solution of Large Linear Systems (1999), North-Holland, Amsterdam
26. Meurant G. The computation of bounds for the norm of the error in the conjugate gradient algorithm. Numer. Algorithms 16-1 (1998) 77-87
27. Golub G., and Meurant G. Matrices, moments and quadrature II: how to compute the norm of the error in iterative methods. BIT 37-3 (1997) 687-705
28. Pernice M., and Walker H. NITSOL: a Newton iterative solver for nonlinear systems. SIAM J. Sci. Comput. 19 (1998) 302-318
29. Rathinam M., and Petzold L. Dynamic iteration using reduced order models: a method for simulation of large scale modular systems. SIAM J. Numer. Anal. 40 (2002) 1446-1474
30. Rathinam M., and Petzold L. A new look at proper orthogonal decomposition. SIAM J. Numer. Anal. 41 (2003) 1893-1925
31. Risler F., and Rey Ch. Iterative accelerating algorithms with Krylov subspaces for the solution to large-scale nonlinear problems. Numer. Algorithms 2 1 (2000) 1-30
32. Rossi T., and Toivanen J. A parallel fast direct solver for the discrete solver for block tridiagonal systems with separable matrices of arbitrary dimension. SIAM J. Sci. Comp. 20 (1999) 1778-1793
33. Saad Y. Iterative Methods for Sparse Linear Systems (1996), PWS Publishing Co., Boston
34. M. Schefer, S. Turek, Benchmark computations of laminar flow around a cylinder, in: E.H. Hirschel (Ed.), Flow Simulation with High-Performance Computers II, Notes on Numerical Fluid Mechanics, vol. 52, Vieweg, 1996, pp. 547-566.
35. D. Tromeur-Dervout, Y. Vassilevski, Fully implicit solution of nonlinear PDEs using POD basis on metacomputing architecture, preprint CDCSP-0500, 2005.
36. D. Tromeur-Dervout, Résolution des Equations de Navier-Stokes en Formulation Vitesse Tourbillon sur Systèmes multiprocesseurs à Mémoire Distribuée, Thesis, Univ. Paris VI, 1993.